I'm really new using OpenFoam but I guess you only have to add U, phi, rho or psi if you have set or calculated initial BC for those! (Maybe with potentialFoam)
And it is also depending on incompressible or compressible simulation. Either you have a field for compressible simulations or just the value in the transport properties.
If you don't add them they will be calculated automatically.
And I also guess that psi is about particle movement depending on the velocity (streamfunction) and directly depending on rho so if you fix one of them the other will be calculated!